The problem of packing as many subgraphs isomorphic to $H \in \mathcal H$ as possible in a graph for a class $\mathcal H$ of graphs is well studied in the literature. Both vertex-disjoint and edge-disjoint versions are known to be NP-complete for $H$ that contains at least three vertices and at least three edges, respectively. In this paper, we consider ``list variants'' of these problems: Given a graph $G$, an integer $k$, and a collection $\mathcal L_{\mathcal H}$ of subgraphs of $G$ isomorphic to some $H \in \mathcal H$, the goal is to compute $k$ subgraphs in $\mathcal L_{\mathcal H}$ that are pairwise vertex- or edge-disjoint. We show several positive and negative results, focusing on classes of sparse graphs, such as bounded-degree graphs, planar graphs, and bounded-treewidth graphs.

翻译：在文献中，对于一类图$\mathcal H$，在一个图中打包尽可能多同构于$H \in \mathcal H$的子图的问题已得到广泛研究。已知当$H$分别包含至少三个顶点和至少三条边时，顶点不相交和边不相交版本都是NP完全的。在本文中，我们考虑这些问题的“列表变体”：给定一个图$G$、一个整数$k$，以及一个由$G$中同构于某个$H \in \mathcal H$的子图组成的集合$\mathcal L_{\mathcal H}$，目标是计算$\mathcal L_{\mathcal H}$中成对顶点不相交或边不相交的$k$个子图。我们展示了若干正面与负面结果，重点关注稀疏图类，如有界度图、平面图和有界树宽图。